A small sphere reaches terminal settling speed when its buoyancy-corrected weight balances viscous drag.
Difficulty
Intermediate
Read time
4 min
Prerequisites
Consistent SI units, algebra, and the physical assumptions listed below
Source
Teng-Jui Lin — Equation SheetsAdapted from Teng-Jui Lin, Equation Sheets — Mechanical Engineering, under CC BY 4.0.
Adapted notation and added original explanations, variables, assumptions, applications, and a worked example. Explicitly required Re_p ≪ 1; the worked case gives Re_p = 0.000654.
A small sphere reaches terminal settling speed when its buoyancy-corrected weight balances viscous drag. The Stokes expression requires creeping flow; the computed speed must be checked against a particle Reynolds number rather than assumed valid.
| Symbol | Meaning | Units |
|---|---|---|
| Signed terminal settling velocity, downward positive | ||
| Sphere radius | ||
| Sphere density | ||
| Fluid density | ||
| Gravitational acceleration | ||
| Fluid dynamic viscosity |
Estimate slow settling in viscous liquids.
Interpret a small-sphere terminal-speed measurement.
A sphere of radius 0.10 mm and density 2500 kg/m³ settles in a fluid of density 1000 kg/m³ and viscosity 0.10 Pa·s. Use g = 9.81 m/s².
Adapted from Teng-Jui Lin, Equation Sheets — Mechanical Engineering, under CC BY 4.0.
Adapted notation and added original explanations, variables, assumptions, applications, and a worked example. Explicitly required Re_p ≪ 1; the worked case gives Re_p = 0.000654.
Assumptions
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